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Published: 
July 21, 2000

Keywords: 
origami, algebraic numbers, pencil of conics, Pythagorean numbers

Subject: 
11R04, 12F05, 51M15, 51N20

Abstract:

In this article we give a simplified set of axioms for
mathematical origami and numbers. The axioms are hierarchically
structured so that the addition of each axiom, allowing new
geometrical
complications, is mirrored in the field theory of the possible
constructible numbers. The fields of Thalian, Pythagorean, Euclidean
and
Origami numbers are thus obtained using this set of axioms. The other
new ingredient here relates the last axiom to the algebraic geometry
of
pencils of conics. It is hoped that the elementary nature of this
article will also be useful for advanced algebra students in
understanding more of the relations of field theory with elementary
geometry.

Author information:
Department of Mathematics and Computer Science, San Jose State University, San Jose, CA 95192 USA
alperin@mathcs.sjsu.edu
http://www.mathcs.sjsu.edu/faculty/alperin
 